Synchronized Chaos in Coupled Optical Feedback Networks

Briana E. Mork, Gustavus Adolphus CollegeKatherine R. Coppess, University of Michigan

Kitzbichler (2009) PLoS Comput Biol 5(3)

Natural dynamical system:Chaos; order and randomness

Oscillators (Nodes)Synchrony

http://2.bp.blogspot.com/-73jjFxeZhjc/T-IRe264OII/AAAAAAAADXU/2PBDgyH2Ufk/s400/Brain_Highways.png

Man-made dynamical system:Periodic (mostly)

Oscillators (Nodes)Synchrony

http://www.efoodsdirect.com/blog/wp-content/uploads/2013/10/power-grid-drill.jpg

Examples of Four-Node Network Topologies

Experimental Four-Node Network Topologies

CRS Williams et al. CHAOS 23, 043117 (2013)

Previously studied

Summer 2014

The Experiment

Four nodes form a delay-coupled system with weighted and directed links. Weight is determined by the coupling strength ε as implemented by the DSP board.

CRS Williams et al. CHAOS 23, 043117 (2013)

Changing the feedback strength β of a node varies the dynamics of the node.

Dynamics of a Nodex(

t) (A

.U.)

time (ms)

CRS Williams et al. CHAOS 23, 043117 (2013)

Experimental Network Topologies

Bidirectional ring

Bidirectional chain with

unidirectional links

Bottom: Laplacian coupling matrices for the two networks, respectively.

Bidirectional Ring

Bidirectional Ring

Bidirectional Chain with

Unidirectional Links

- Stability analysis for synchronous states- Many-node networks- Comparison of convergence rates between global and cluster synchrony

Conclusions

Future work

- The synchronous states that arise depend on topology of the network.- Transitions between synchronous states depend on coupling strength.

Caitlin R. S. Williams, Washington and Lee UniversityAaron M. Hagerstrom, University of Maryland

Louis Pecora, Naval Research LaboratoryFrancesco Sorrentino, University of New Mexico

Thomas E. Murphy, University of MarylandRajarshi Roy, University of Maryland

Acknowledgments

Synchronization states and multistability in a ring of periodic oscillators: Experimentally variable coupling delays CRS Williams et al. CHAOS 23, 043117 (2013)

Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators CRS Williams et al. PRL 110, 064104 (2013)

Cluster Synchronization and Isolated Desynchronization in Complex Networks with Symmetries L Pecora et al. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5079 (2014)

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